Time-optimal trajectories for robotic transfer devices

ABSTRACT

A time-optimal trajectory generation method, for a robotic manipulator having a transport path with at least one path segment, comprising generating a forward time-optimal trajectory of the manipulator along the at least one path segment from a start point of the at least one path segment towards an end point of the at least one path segment, generating a reverse time-optimal trajectory of the manipulator along the at least one path segment from the end point towards the start point of the at least one path segment, and combining the time-optimal forward and reverse trajectories to obtain a complete time-optimal trajectory, where the forward and reverse trajectories of the at least one path segment are blended together with a smoothing bridge joining the time-optimal forward and reverse trajectories in a position-velocity reference frame with substantially no discontinuity between the time-optimal forward and reverse trajectories.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the National Stage of International Application No.PCT/US2012/052977 having International Filing date, 30 Aug. 2012, whichdesignated the United States of America, and which InternationalApplication was published under PCT Article 21 (s) as WO Publication2013/033289 A1 and which claims priority from, and benefit of U.S.Provisional Application No. 61/530,651 filed on 2 Sep. 2011, thedisclosures of which are incorporated herein by reference in theirentireties.

BACKGROUND

1. Field

The exemplary embodiments generally relate to robotic manipulators and,more particularly, to a method and means for the generation of smoothtime-optimal trajectories for robotic manipulators.

2. Brief Description of Related Developments

Trajectory generation is typically used when transferring substratesheld by a robotic manipulator from one place to another. While roboticsystems for carrying light payloads can be over-designed to providenecessary torque margins, increased peak torque requirements become afactor for performance, size, cost and life of both direct-drive andharmonic-drive robotic manipulators for high or heavy payloads.Conventional trajectory generation methods generally do not account fortorque constraints or do not produce a smooth commanded trajectory. Forexample, a well known servo control approach can be found in the paperentitled “Time-optimal control of robotic manipulators along specifiedpaths” from Bobrow et al. (International Journal of Robotic Research,Vol. 4, No. 3, 1985), which generally operates to establish switchingpoints between acceleration and deceleration of a robot end effectorwithout exceeding a maximum tolerable velocity. The switching pointsgenerally operate to change the system state in minimum time while atall times using all available system power. This approach is sometimesalso referred to as bang-bang control.

While time-optimal, some real world applications can limit the viabilityof this approach due to the presence of variable or unquantifiablesystem resonances. More particularly, abrupt changes in jerk (change inacceleration with respect to time) can serve as a broad spectrumexcitation of the system, resulting in unacceptably long settle times atthe final position.

Conventional systems to remove discontinuities in trajectories frombang-bang control, such as Bobrow et al., by constraining trajectoryprofiles or kinematic characteristics of the trajectory profiles such asacceleration, jerk and jerk rate result in non-optimal trajectories andhence lower efficiencies. This is especially so for robotic systemsconfigured to handle large, heavier payloads.

It would be advantageous to provide trajectory generation that, e.g.,uses maximum system torque and payload accelerations and provides smoothcommand time-optimal trajectories.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and other features of the disclosed embodimentsare explained in the following description, taken in connection with theaccompanying drawings, wherein:

FIG. 1 is a schematic illustration of a processing tool incorporatingaspects of the disclosed embodiment;

FIG. 2 is a schematic illustration of another processing toolincorporating aspects of the disclosed embodiment;

FIGS. 3A-3D are exemplary substrate transport paths to which aspects ofthe disclosed embodiment may be applied;

FIG. 4 illustrates an “S-curve profile” of a conventional trajectory ofa robot arm;

FIG. 5A is an exemplary graph illustrating a time-optimized trajectoryin accordance with an aspect of the disclosed embodiment;

FIG. 5B is a flow chart illustrating the generation of time-optimaltrajectory in accordance with an aspect of the disclosed embodiment;

FIGS. 5C and 5D are exemplary graphs illustrating time-optimizedtrajectories in accordance with aspects of the disclosed embodiment;

FIG. 6A is an exemplary graph illustrating motor torque in atime-optimal trajectory generated in accordance with an aspect of thedisclosed embodiment;

FIG. 6B is an exemplary graph illustrating an end effector accelerationprofile in a time-optimal trajectory generated in accordance with anaspect of the disclosed embodiment;

FIG. 7A is an exemplary graph illustrating an acceleration plot versustime in accordance with an aspect of the disclosed embodiment; and

FIGS. 7B and 7C are exemplary graphs illustrating motor torque plotsversus time in accordance with aspects of the disclosed embodiment.

DETAILED DESCRIPTION

FIG. 1 illustrates an exemplary substrate processing apparatus in whichaspects of the disclosed embodiment can be used. Although the aspects ofthe disclosed embodiment will be described with reference to thedrawings, it should be understood that the disclosed embodiment can beembodied in many alternate forms. In addition, any suitable size, shapeor type of elements or materials could be used.

As can be seen in FIG. 1, a substrate processing apparatus, such as forexample a semiconductor tool station 690 is shown in accordance with anaspect of the disclosed embodiment. Although a semiconductor orsubstrate processing tool is shown in the drawings, the aspects of thedisclosed embodiment described herein can be applied to any tool stationor application employing robotic manipulators. The substrate processingtool 690 may include different sections having, for example, differentatmospheres separated by, for example, a load lock 610 (e.g. inert gason one side and vacuum on the other, or atmospheric clean air on oneside and vacuum/inert gas on the other). In one aspect the tool 690 isshown as a cluster tool, however aspects of the disclosed embodimentsmay be applied to any suitable tool station such as, for example, alinear tool station such as that shown in FIG. 2 and described in U.S.patent application Ser. No. 11/442,511, entitled “Linearly DistributedSemiconductor Workpiece Processing Tool,” filed May 26, 2006, thedisclosure of which is incorporated by reference herein in its entirety.Other exemplary substrate processing tools in which aspects of thedisclosed embodiment may be used include but are not limited to U.S.patent application Ser. No. 12/123,329 filed May 19, 2008; U.S. patentapplication Ser. No. 12/123,365 filed May 19, 2008; U.S. patentapplication Ser. No. 12/330,780 filed Dec. 9, 2008; U.S. patentapplication Ser. No. 13/159,034 filed Jan. 13, 2011; U.S. patentapplication Ser. No. 12/542,588 filed Aug. 17, 2009; and U.S. Pat. Nos.7,575,406; 7,959,395; and 7,988,398 all of which are incorporated byreference herein in their entireties. The tool station 690 generallyincludes an atmospheric front end 600, a vacuum load lock 610 and avacuum back end 620. In other aspects of the disclosed embodiment, thetool station may have any suitable configuration. The components of eachof the front end 600, load lock 610 and back end 620 may be connected toa controller 691 which may be part of any suitable control architecturesuch as, for example, a clustered architecture control. The controlsystem may be a closed loop controller having a master controller,cluster controllers and autonomous remote controllers such as thosedisclosed in U.S. patent application Ser. No. 11/178,615, entitled“Scalable Motion Control System,” filed Jul. 11, 2005 (now U.S. Pat. No.7,904,182), the disclosure of which is incorporated by reference hereinin its entirety. In other aspects of the disclosed embodiment, anysuitable controller and/or control system may be utilized. Thecontroller of the processing tool, such as controller 691, or any othersuitable controller connected to the substrate processing tool mayinclude a processor and/or a memory configured to generate the optimaltrajectories as described herein. In one aspect the controller 691 maybe configured for what is known as being a “bang-bang” controller thatcontrols the robotic transport such that all available power is used(e.g. max torque) to effect motion of the robotic transport as otherwisefurther described below.

In one aspect, the front end 600 generally includes load port modules605 and a mini-environment 660 such as for example an equipment frontend module (EFEM). The load port modules 605 may be box opener/loader totool standard (BOLTS) interfaces that conform to SEMI standards E15.1,E47.1, E62, E19.5 or E1.9 for 300 mm load ports, front opening or bottomopening boxes/pods and cassettes. In alternate embodiments, the loadport modules may be configured as 200 mm wafer interfaces, 400 mm waferinterfaces, or any other suitable substrate interfaces such as forexample larger or smaller wafers or flat panels for flat panel displays,LED (light emitting diode) panels and solar panels. Although two loadport modules are shown in FIG. 1, in other aspects of the disclosedembodiment any suitable number of load port modules may be incorporatedinto the front end 600. The load port modules 605 may be configured toreceive substrate carriers or cassettes 650 from an overhead transportsystem, automatic guided vehicles, person guided vehicles, rail guidedvehicles or from any other suitable transport method. The load portmodules 605 may interface with the mini-environment 660 through loadports 640. The load ports 640 may allow the passage of substratesbetween the substrate cassettes 650 and the mini-environment 660. Themini-environment 660 generally includes a transfer robot (not shown) fortransporting the substrates from the cassettes 650 to, for example, theload lock 610. In one aspect, the transfer robot may be a track mountedrobot such as that described in, for example, U.S. Pat. No. 6,002,840,the disclosure of which is incorporated by reference herein in itsentirety or any other suitable transfer robot including but not limitedto SCARA (Selective Compliant Articulated Robot Arm) robots, frog-legrobots, linear sliding arm robots and four bar-link robots where therobotic manipulators have one or more arms each having one or more endeffectors or substrate holders (e.g. each may be capable holding one ormore substrates). Other suitable examples of robots include those foundin U.S. patent application Ser. No. 11/148,871 filed on Jun. 9, 2005;U.S. patent application Ser. No. 11/179,762 filed on Jul. 11, 2005; U.S.patent application Ser. No. 12/117,415 filed May 8, 2008; U.S. patentapplication Ser. No. 12/117,355 filed May 8, 2008; U.S. patentapplication Ser. No. 13/219,267 filed Aug. 26, 2011 (now U.S. Pat. No.8,237,391); U.S. patent application Ser. No. 13/030,856 filed Feb. 18,2011; and U.S. Pat. Nos. 8,008,884; 6,547,510; 5,813,823; 5,899,658;5,720,590; and 7,891,935 all of which are incorporated by referenceherein in their entireties. The mini-environment 660 may provide acontrolled, clean zone for substrate transfer between multiple load portmodules.

The vacuum load lock 610 may be located between and connected to themini-environment 660 and the back end 620. The substrate holdingchamber(s) of the load lock 610 generally includes atmospheric andvacuum slot valves. Each slot valve of the chamber(s) may beindependently closable by a suitable door(s) of the slot valve. The slotvalves may provide the environmental isolation employed to evacuate theload lock 610 after loading a substrate from the atmospheric front end600 and to maintain the vacuum in the transport chamber 625 when ventingthe lock with an inert gas such as nitrogen. In one aspect the load lock610 may also include an aligner for aligning a fiducial of the substrateto a desired position for processing, a substrate buffer or any othersuitable processing apparatus. In other aspects of the disclosedembodiment, the vacuum load lock may be located in any suitable locationof the processing apparatus and have any suitable configurationincluding any suitable substrate processing equipment.

The vacuum back end 620 generally includes transport chamber 625, one ormore processing station(s) 630 and a transfer robot (not shown). Thetransfer robot may be located within the transport chamber 625 totransport substrates between the load lock 610 and the variousprocessing stations 630 and be substantially similar to the transferrobot described above with respect to the mini-environment 660 but forthe use of the robot in a vacuum environment. The processing stations630 may operate on the substrates through various deposition, etching,or other types of processes to form electrical circuitry or otherdesired structure on the substrates. Typical processes include but arenot limited to thin film processes that use a vacuum such as plasma etchor other etching processes, chemical vapor deposition (CVD), plasmavapor deposition (PVD), implantation such as ion implantation,metrology, rapid thermal processing (RTP), dry strip atomic layerdeposition (ALD), oxidation/diffusion, forming of nitrides, vacuumlithography, epitaxy (EPI), wire bonder and evaporation or other thinfilm processes that use vacuum pressures. The processing stations 630are connected to the transport chamber 625 to allow substrates to bepassed from the transport chamber 625 to the processing stations 630 andvice versa.

Referring now to FIG. 2, another exemplary substrate processing tool 710having different sections is shown. In this aspect, the processing toolis a linear processing tool where the tool interface section 712 ismounted to a transport chamber module 718 so that the interface section712 is facing generally towards (e.g. inwards) but is offset from thelongitudinal axis X of the transport chamber 718T. The transport chambermodule 718 may be extended in any suitable direction to extend a lengthof the transport chamber 718T by attaching other transport chambermodules 718A, 718I, 718J to interfaces 750, 760, 770 as described inU.S. patent application Ser. No. 11/442,511, previously incorporatedherein by reference. The interfaces 750, 760, 770 may be substantiallysimilar to the load lock described above with respect to processing tool690. Each transport chamber module 718, 719A, 718I, 718J includes asuitable substrate transport 780 for transporting substrates throughoutthe processing system 710 and into and out of, for example, processingmodules PM. In one aspect the transport 780 may be substantially similarto those described above. As may be realized, each chamber module may becapable of holding an isolated or controlled atmosphere (e.g. N2, cleanair, vacuum). In other aspects, the transport chamber modules 718, 719A,718I, 718J may include features of the load lock 610 as describedherein.

Referring now to FIGS. 3A-3D, exemplary transport paths of a substrateon an end effector of a robotic transport are shown in accordance withaspects of the disclosed embodiment. As may be realized these transportpaths may be for any suitable robotic transport such as, for example,the robotic transports described above. As may also be realized atime-optimal trajectory may be generated in accordance with aspects ofthe disclosed embodiments for each of these exemplary transport paths.It is noted that the term “path” as used herein and depicted in thedrawings refers to the physical transport paths of the substratesthrough a three-dimensional space between substrate holding locations.It is noted that the paths may include one or more segments that arejoined to each other to form the path. The term “trajectory” of the pathincludes the kinematic properties of the substrate transport or at leasta portion thereof (e.g. the end effector, arm links, drive motor, etc.)such as acceleration, velocity, etc. moving along the transport path.

As can be seen in FIG. 3A one suitable substrate transport path 300 maybe a rectilinear transport path having, for example, two segments 300Aand 300B where each segment is substantially a straight line so that thesubstrate travels along the rectilinear path formed by the segments300A, 300B. Another suitable transport path 310, shown in FIG. 3B, mayhave at least a portion of the path be a curved or non-linear where thesubstrate movement between segments 310A and 310B is blended so that thesubstrate follows a substantially smooth curve for transitioning betweenthe segments 310A and 310B. FIGS. 3C and 3D illustrate compound paths320, 330 that may include any suitable number of rectilinear transportsegments and/or curved (i.e. non-linear) transport segments that may ormay not be blended together. For example, FIG. 3C illustrates atransport path 320 having three segments where segments 320A and 320Bmeet at point 13 and segments 320B and 320C meet at point 23. FIG. 3Dillustrates path 330 having three segments 330A, 330B, 330C where thesegments are joined respectively at points 15 and 25. However, in FIG.3D the transition between segments 330A and 330B and between segments330B and 330C are blended by any suitable smooth transition curve. Asmay be realized, in other aspects, the transport paths may be anysuitable transport paths including one or more segments forming anysuitably shaped path for transporting substrates between any suitablesubstrate holding stations (e.g. an initial/starting point and afinal/ending point). The path can have any suitable shape, and thetrajectory along the path (e.g. the kinematic properties) may beestablished in the linear frame of reference for the path. As may alsobe realized the transport paths may be two-dimensional orthree-dimensional transport paths including any suitable number of pathssegments that are combined and/or blended to form an optimal pathbetween the starting and ending points of the path.

As described above, any suitable controller, such as controller 691, maybe configured as a bang-bang controller for generating time-optimalmotions of at least a portion of the robotic transport, such as the endeffector, using maximum power of the robotic transport drive. It isnoted the aspects of the disclosed embodiment allow for the generationof otherwise unparameterized substrate transport trajectories havingmotor torque (e.g. maximum torque/peak torque) and/or substrateacceleration constraints for, e.g., high payload applications or anyother suitable payload applications. The term unparameterized as usedherein with respect to the generated trajectories means that thetrajectory is unconstrained as to the curve or shape of the trajectory(either with respect to time or in the position-velocity reference frameor space) such that a time-optimal trajectory shape is achieved withinthe noted constraints of available maximum motor torque (e.g. themaximum torque as specified by the motor manufacturer) of the roboticmanipulator, a maximum substrate acceleration limit (e.g. a point atwhich the substrate begins to slip on the substrate holder of therobotic manipulator), and/or a maximum velocity limit. In accordancewith the aspects of the disclosed embodiments trajectories can begenerated for each of the path segments such that optimal (shortest)move times (e.g. substrate transport times between a starting and endingpoint) are achieved for given maximum drive torque constraints. Further,peak torque requirements for drive components, such as motors andharmonic gear boxes, can be reduced (with or without the shorter movetimes) leading to lower costs associated with the robotic transport,reduced size of the robotic transport and/or increased life of therobotic transport. The aspects of the disclosed embodiment address thedeficiencies of existing trajectory generation methods which generallydo not take into consideration torque constraints or generally do notproduce a smooth commanded trajectory. The term “smoothness” as usedherein with respect to the generated trajectories refers to a continuousacceleration over time. It is noted that a discontinuity in accelerationis generally not practically achievable and undesired resulting inexcitation of natural vibration modes of, for example, the arm of therobotic transport as well as significant tracking errors.

In one aspect of the disclosed embodiment referring to FIG. 5A, atime-optimal trajectory (which may also be referred to as atorque-optimal trajectory) that operates to change the state of thesystem in minimum time, e.g. using maximum available torque, may begenerated for each segment of the substrate transport path (thetransport path may have more than one set of segments as illustrated ine.g. FIGS. 3C and 3D), where the time-optimal trajectory may be obtainedby generating at least a portion of a time-optimal forward trajectory550 from the start point (e.g. in the position-velocity reference frame)(Block 500, FIG. 5B), generating at least a portion of a time-optimalreverse trajectory 560 from the end point (e.g. in the position-velocityreference frame) (Block 510, FIG. 5B), and combining the forward andreverse trajectories to generate the complete time-optimal trajectory(Block 520, FIG. 5B). It is noted that the portions of the time-optimalforward and reverse trajectories can be generated in any suitable orderand not necessarily in the order listed above. It is also noted that thetime-optimal forward and reverse trajectories may be any suitableoptimal trajectories based on, for example, the motor torque, substrateacceleration and/or velocity constraints described herein. In oneaspect, only the portions of the time-optimal forward and reversetrajectories between the respective start and end points and the apex ofthe trajectory may be generated while in other aspects the completetime-optimal forward and reverse trajectories may be generated. Theaspects of the disclosed embodiment provide for the combination of theforward and reverse trajectories such that a smoothing “bridge” segment570 joins a point on the forward trajectory to a point on the reversetrajectory. The time duration of this bridge segment 570 may be obtainedin any suitable manner such as by the integral of the inverse of thevelocity with respect to position so that the bridge segment satisfiesthe acceleration continuity condition at its endpoints. In one aspectthe smoothing bridge 570 is a mathematical blending algorithm thatsubstantially eliminates discontinuity between the forward and reversetrajectories 550, 560. In one aspect the smoothing bridge 570 maymathematically be a quadratic Bezier curve in the position-velocityreference frame but it should be understood that in other aspects thesmoothing bridge 570 may be any other suitable curve or roundingapproach such as, for example, a third order Bezier curve or a cubicspline. The smoothing curve 570, such as for example, the Bezier curvemay be an algorithm that is fit/splined through a numerical solutionbetween the forward and reverse trajectories.

Referring to FIG. 4, an illustration of a “trapezoidal velocity profile”and a “S-curve profile” for minimizing substrate transfer time areshown. These plots show velocity with respect to time curves forcommanded velocity at the robot arm drive motor. However, thetrapezoidal velocity profile and S-curve profile are not time-optimalwhen compared with the trajectories generated in accordance with theaspects of the disclosed embodiment. As can be seen in FIG. 4 there areportions of the S-curve and trapezoidal curve where the velocity (andhence the acceleration) are constant such that maximum available poweris not used when generating the trajectory).

With reference again to FIG. 5A an exemplary illustration of atrajectory generated in accordance with the aspects of the disclosedembodiment is shown. For non-limiting exemplary purposes only, themotion profiles are generated for a radial extend motion for a SCARA armrobotic manipulator. In this example, again for non-limiting exemplarypurposes only, the trajectory is constrained by a maximum R-motor (e.g.radial extension motor) torque limit of about 5 Nm and a maximumsubstrate acceleration limit of about 0.3 g. A radial extension of about400 mm of the robot arm is considered in FIG. 5A.

FIG. 5A illustrates the optimal trajectory of, for example, FIGS. 7A-7C(described below) in a position-velocity reference frame. As can be seenin FIG. 5A the forward trajectory segment 550, the reverse trajectorysegment 560, and the bridging segment 570 are shown. In one aspect, ateach of the points of contact or interfaces 10, 20 with the forward andreverse trajectory segments 550, 560, the bridging segment 570 hassubstantially the same tangent and amplitude as a respective one of theforward and reverse trajectory segments 550, 560. As described above, inone aspect the bridging or bridge segment 570 may be defined as aquadratic Bezier curve (but in other aspects the bridge segment may bedefined in any suitable manner by any suitable curve such as, forexample, a third order Bezier curve) in which the position p andvelocity v are defined in terms of the position and velocity at points10, 20 and a, where a is defined as the point of intersection of thetangents of the forward and reverse trajectories 550, 560 at points 10and 20. In one aspect the position p and velocity v may be defined asfollows:

p(τ)=p ₁(1−τ)²+2p _(a)(1−τ)τ+p ₂τ²  [1]

v(τ)=v ₁(1−τ)²+2v _(a)(1−τ)τ+v ₂τ²  [2]

where the parameter τ varies from 0 to 1. The progression of time can beobtained as a function of the parameter τ as follows:

$\begin{matrix}{{t(\tau)} = {\int_{0}^{\tau}{\frac{p}{\tau}\frac{1}{v}{\tau}}}} & \lbrack 3\rbrack\end{matrix}$

It is noted that the points 10 and 20 are chosen so that thecharacteristics of the trajectory curve (e.g. velocity, change invelocity and rate of change in velocity) at all points in the bridgesegment are equal to or below the corresponding characteristics of theforward and reverse segments as extending respectively forward andreverse from the corresponding points 10, 20 (e.g. looking at FIG. 5Athe bridge segment remains underneath the extensions of each of theforward and reverse trajectories that intersect at point a, and relatedcharacteristics of the bridge segment such as slope and change in slopeare below comparable characteristics of the respective extensions atcorresponding points 10, 20). The curve forming the bridge segment mayprovide any suitable number of degrees of freedom that allows for thesatisfaction of the above velocity condition without changing the startand end points. It is again noted that while the aspects of thedisclosed embodiment are illustrated with respect to a linear radialmotion of the substrate holder, it should be understood that the aspectsof the disclosed embodiment is extendable to motion along non-linearpaths. The aspects of the disclosed embodiments may also be applied tomultiple corner points that need to be smoothed in a given trajectory.For example, referring to FIG. 5C a time-optimal trajectory is shownwhere a central region of the trajectory curve 573 (that may begenerated, for example, either as a forward trajectory or a reversetrajectory) has a reduced velocity due to, for example a constraint onvelocity in this region of the trajectory. In this aspect there are twopoints a, b that are to be smoothed in accordance with aspects of thedisclosed embodiments. Here, the forward trajectory 551 is generated ina manner substantially similar to that described above from a respectivestart point. The reverse trajectory 563 is also generated in a mannersubstantially similar to that described above from a respective endpoint. It is also noted that while the trajectory curve 573 is shown ashaving a concave shape or slope in other aspects the trajectory may havea convex slope or a combination of a convex and concave slope as shownin FIG. 5D (see trajectory 573′) so that the portions of the trajectorycurve 573′ intersecting trajectories 551, 563 have a convex slope andthe central portion of trajectory curve 573′ has a concave slope. Thepoints a and b are bridged in a manner substantially similar to thatdescribed above such that the characteristics of the trajectory curves(e.g. velocity, change in velocity and rate of change in velocity)corresponding to bridge segments 571, 572 at all points in the bridgesegment are equal to or below (as may be seen in FIGS. 5A, 5C and 5D)the corresponding characteristics of the forward and reverse segments asextending respectively forward and reverse from the corresponding points10, 20, 30, 40 (e.g. looking at FIGS. 5C and 5D the bridge segmentsremain underneath the extensions of each of the forward and reversetrajectories that intersect at point a and point b and relatedcharacteristics of the bridge segments such as slope and change in slopeare below comparable characteristics of the respective extensions atcorresponding points 10, 20, 30, 40).

FIG. 6A is an exemplary graph illustrating a comparison of motor torquein an optimal trajectory with and without the bridge segment. FIG. 6B isan exemplary graph illustrating a comparison of a substrate holderacceleration profile within the trajectory with and without the bridgesegment.

Referring now to FIGS. 7A-7C, FIG. 7A compares the substrateacceleration profiles using a time-optimized trajectory in accordancewith an aspect of the disclosed embodiment with a standard S-curvetrajectory (see also FIG. 4) generated for the end effector or substrateholder motion where the substrate holder is connected to the arm of therobotic manipulator (see FIG. 2 which illustrates a substrate holderconnected to a SCARA type robotic arm). The motor torques for the twotrajectories (e.g. the time-optimized trajectory and the S-curvetrajectory) are shown in FIG. 7B. As can be seen in FIGS. 7A and 7B thetime-optimized trajectory optimally utilizes the available motor torquesuch that the move time of the time-optimized trajectory isapproximately 25 percent less than the move time of the standard S-curvetrajectory. As such, the trajectory illustrated in FIGS. 7A and 7B maybe considered a time-optimal trajectory that includes an optimizedtorque. FIG. 7C compares the time-optimized trajectory and the standardS-curve trajectory where each trajectory is generated so that the movetimes are substantially the same. As can be seen in FIG. 7C, forsubstantially the same move time, the time-optimized trajectory requiresabout 50 percent less torque than the standard S-curve trajectorygenerated for the substrate holder motion.

In accordance with one or more aspects of the disclosed embodiment atime-optimal trajectory generation method is provided for a roboticmanipulator having a transport path with at least one path segment. Themethod includes generating a forward time-optimal trajectory of themanipulator along the at least one path segment from a start point ofthe at least one path segment towards an end point of the at least onepath segment, generating a reverse time-optimal trajectory of themanipulator along the at least one path segment from the end point ofthe at least one path segment towards the start point of the at leastone path segment and combining the time-optimal forward and reversetrajectories to obtain a complete time-optimal trajectory, where theforward and reverse trajectories of the at least one path segment areblended together with a smoothing bridge joining the time-optimalforward and reverse trajectories in a position-velocity reference framewith substantially no discontinuity between the time-optimal forward andreverse trajectories.

In accordance with one or more aspects of the disclosed embodiment, thecomplete time-optimal trajectory is unparameterized.

In accordance with one or more aspects of the disclosed embodiment, atleast one of the time-optimal forward and reverse trajectory is definedby a maximum motor torque of the robotic manipulator.

In accordance with one or more aspects of the disclosed embodiment, thesmoothing bridge is connected to each of the time-optimal forward andreverse trajectories at respective end points of the smoothing bridge,where each end point of the smoothing bridge is tangent to a respectiveone of the time-optimal forward and reverse trajectories at therespective end points in the position-velocity reference frame. Inaccordance with one or more aspects characteristics of a trajectory ofthe smoothing bridge at all points in the smoothing bridge are equal toor below corresponding characteristics of the forward and reversetrajectories as extending respectively forward and reverse from therespective end points.

In accordance with one or more aspects of the disclosed embodiment, thecomplete time-optimal trajectory is substantially independent of thetransport path.

In accordance with one or more aspects of the disclosed embodiment, theacceleration along the transport path is substantially continuous forand between the time-optimal forward trajectory, the time-optimalreverse trajectory and the smoothing bridge.

In accordance with one or more aspects of the disclosed embodiment, thesmoothing bridge is a numerical solution that fits a curve between theforward and reverse trajectories. In one aspect, the smoothing bridgecomprises a quadratic Bezier curve, a third order Bezier curve or cubicspline.

In accordance with one or more aspects of the disclosed embodiment, arespective complete time-optimal trajectory including a respectivesmoothing bridge is generated for each of the at least one pathsegments.

In accordance with one or more aspects of the disclosed embodiment, themethod further includes blending the endpoints of adjacent ones of theat least one path segment together with a smoothing bridge.

In accordance with one or more aspects of the disclosed embodiment asubstrate processing tool is provided. The substrate processing toolincludes a robotic manipulator including a substrate holder that travelsalong a transport path having at least one path segment and a controllerconnected to the robotic manipulator. The controller is configured togenerate a time-optimal forward trajectory of the robotic manipulatoralong the at least one path segment from a start point of the at leastone path segment towards an end point of the at least one path segment,generate a time-optimal reverse trajectory of the robotic manipulatoralong the at least one path segment from the end point of the at leastone path segment towards the start point of the at least one pathsegment and combine the time-optimal forward and reverse trajectories toobtain a complete time-optimal trajectory, where the time-optimalforward and reverse trajectories of the at least one path segment areblended together with a smoothing bridge joining the time-optimalforward and reverse trajectories in a position-velocity reference framewith substantially no discontinuity between the time-optimal forward andreverse trajectories.

In accordance with one or more aspects of the disclosed embodiment, thecomplete time-optimal trajectory is unparameterized.

In accordance with one or more aspects of the disclosed embodiment, atleast one of the time-optimal forward and reverse trajectory is definedby a maximum motor torque of the robotic manipulator.

In accordance with one or more aspects of the disclosed embodiment, thecontroller is configured to connect the smoothing bridge to each of thetime-optimal forward and reverse trajectories at respective end pointsof the smoothing bridge, where each end point of the smoothing bridge istangent to a respective one of the time-optimal forward and reversetrajectories at the respective end points in the position-velocityreference frame. In accordance with one or more aspects characteristicsof a trajectory of the smoothing bridge at all points in the smoothingbridge are equal to or below corresponding characteristics of theforward and reverse trajectories as extending respectively forward andreverse from the respective end points.

In accordance with one or more aspects of the disclosed embodiment, theacceleration along the transport path is substantially continuous forand between the time-optimal forward trajectory, the time-optimalreverse trajectory and the smoothing bridge.

In accordance with one or more aspects of the disclosed embodiment, thesmoothing bridge comprises a quadratic Bezier curve, a third orderBezier curve or a cubic spline.

In accordance with one or more aspects of the disclosed embodiment, thecontroller is configured to generate a complete time-optimal trajectoryincluding a respective smoothing bridge for each of the at least onepath segments.

In accordance with one or more aspects of the disclosed embodiment, thecontroller is further configured to blend the endpoints of adjacent onesof the at least one path segment together with a smoothing bridge.

In accordance with one or more aspects of the disclosed embodiment, thecomplete time-optimal trajectory is substantially independent of thetransport path.

It is noted that the aspects of the disclosed embodiments can be usedindividually or in any suitable combination thereof. It should also beunderstood that the foregoing description is only illustrative of theaspects of the disclosed embodiment. Various alternatives andmodifications can be devised by those skilled in the art withoutdeparting from the aspects of the disclosed embodiment. Accordingly, theaspects of the disclosed embodiment are intended to embrace all suchalternatives, modifications and variances that fall within the scope ofthe appended claims. Further, the mere fact that different features arerecited in mutually difference dependent or independent claims does notindicate that a combination of these features cannot be advantageouslyused, such a combination remaining within the scope of the aspects ofthe invention.

What is claimed is:
 1. A time-optimal trajectory generation method for arobotic manipulator having a transport path with at least one pathsegment, the method comprising: generating a forward time-optimaltrajectory of the manipulator along the at least one path segment from astart point of the at least one path segment towards an end point of theat least one path segment; generating a reverse time-optimal trajectoryof the manipulator along the at least one path segment from the endpoint of the at least one path segment towards the start point of the atleast one path segment; and combining the time-optimal forward andreverse trajectories to obtain a complete time-optimal trajectory, wherethe forward and reverse trajectories of the at least one path segmentare blended together with a smoothing bridge joining the time-optimalforward and reverse trajectories in a position-velocity reference framewith substantially no discontinuity between the time-optimal forward andreverse trajectories.
 2. The method of claim 1, wherein the completetime-optimal trajectory is unparameterized.
 3. The method of claim 1,wherein at least one of the time-optimal forward and reverse trajectoryis defined by a maximum motor torque of the robotic manipulator.
 4. Themethod of claim 1, wherein the smoothing bridge is connected to each ofthe time-optimal forward and reverse trajectories at respective endpoints of the smoothing bridge, where each end point of the smoothingbridge is tangent to a respective one of the time-optimal forward andreverse trajectories at the respective end points in theposition-velocity reference frame.
 5. The method of claim 4, whereincharacteristics of a trajectory of the smoothing bridge at all points inthe smoothing bridge are equal to or below corresponding characteristicsof the forward and reverse trajectories as extending respectivelyforward and reverse from the respective end points.
 6. The method ofclaim 1, wherein the complete time-optimal trajectory is substantiallyindependent of the transport path.
 7. The method of claim 1, wherein theacceleration along the transport path is substantially continuous forand between the time-optimal forward trajectory, the time-optimalreverse trajectory and the smoothing bridge.
 8. The method of claim 1,wherein the smoothing bridge is a numerical solution that fits a curvebetween the forward and reverse trajectories.
 9. The method of claim 8,wherein the smoothing bridge comprises a quadratic Bezier curve, a thirdorder Bezier curve or cubic spline.
 10. The method of claim 1, wherein arespective complete time-optimal trajectory including a respectivesmoothing bridge is generated for each of the at least one pathsegments.
 11. The method of claim 1, wherein the method further includesblending the endpoints of adjacent ones of the at least one path segmenttogether with a smoothing bridge.
 12. A substrate processing toolcomprising: a robotic manipulator including a substrate holder thattravels along a transport path having at least one path segment; and acontroller connected to the robotic manipulator, the controller beingconfigured to generate a time-optimal forward trajectory of the roboticmanipulator along the at least one path segment from a start point ofthe at least one path segment towards an end point of the at least onepath segment, generate a time-optimal reverse trajectory of the roboticmanipulator along the at least one path segment from the end point ofthe at least one path segment towards the start point of the at leastone path segment, and combine the time-optimal forward and reversetrajectories to obtain a complete time-optimal trajectory, where thetime-optimal forward and reverse trajectories of the at least one pathsegment are blended together with a smoothing bridge joining thetime-optimal forward and reverse trajectories in a position-velocityreference frame with substantially no discontinuity between thetime-optimal forward and reverse trajectories.
 13. The apparatus ofclaim 12, wherein the complete time-optimal trajectory isunparameterized.
 14. The apparatus of claim 12, at least one of thetime-optimal forward and reverse trajectory is defined by a maximummotor torque of the robotic manipulator.
 15. The apparatus of claim 12,wherein the controller is further configured to connect the smoothingbridge to each of the time-optimal forward and reverse trajectories atrespective end points of the smoothing bridge, where each end point ofthe smoothing bridge is tangent to a respective one of the time-optimalforward and reverse trajectories at the respective end points in theposition-velocity reference frame.
 16. The apparatus of claim 15,wherein characteristics of a trajectory of the smoothing bridge at allpoints in the smoothing bridge are equal to or below correspondingcharacteristics of the forward and reverse trajectories as extendingrespectively forward and reverse from the respective end points.
 17. Theapparatus of claim 12, wherein the acceleration along the transport pathis substantially continuous for and between the time-optimal forwardtrajectory, the time-optimal reverse trajectory and the smoothingbridge.
 18. The apparatus of claim 12, the smoothing bridge comprises aquadratic Bezier curve, a third order Bezier curve or a cubic spline.19. The apparatus of claim 12, wherein the controller is furtherconfigured to generate a respective complete time-optimal trajectoryincluding a respective smoothing bridge for each of the at least onepath segments.
 20. The apparatus of claim 12, wherein the controller isfurther configured to blend the endpoints of adjacent ones of the atleast one path segment together with a smoothing bridge.
 21. Theapparatus of claim 12, wherein the complete time-optimal trajectory issubstantially independent of the transport path.